7.11 Topic 11: Inference for Two Proportions 88. The Vegetarian Resource Group commissioned Harris Poll in 2016 to conduct a nationally rep- resentative online poll of 2,015 American adults aged 18 and over. They found that 3.3% of the respondents identified as vegetarian. Food habits in India tend to have a large religious and social component. How does the popularity of the vegetarian diet differ in the US and India? A 2014 survey conducted by the Registrar General of India found that 29% of Indians were vegetarian. Suppose the proportion was obtained from a random sample of 1,000 Indians. (a) Construct and interpret a 99% confidence interval for the difference in proportions of tarians in India and the US. vege- (b) Based on the interval, what kind of evidence do you expect to have for the alternative in a two-sided hypothesis test? Explain. 89. It is hard to persuade consumers to abandon a product with which they are familiar. One experiment gave consumers free samples of a new laundry detergent and also a standard detergent. After some time, ask the subjects which detergent they prefer. Here are the data. User Nonuser Prefer new product Prefer standard product 19 31 29 27 (a) Calculate a 90% confidence interval for the difference in proportions between nonusers and users of the standard detergent that prefer the new detergent. (b) Based on the confidence interval in (a), can we conclude that a significant difference exists between the proportion of nonusers of the standard detergent who prefer the new detergent and the proportion of users of the standard detergent who prefer the new detergent? Explain. 90. Spending on concessions at the movies varies by age of the movie goer. A random sample of 100 adults in their 40's found that 70 purchased popcorn. A random sample of 100 adults less than 40 years old found that 59 purchased popcorn. (a) State the hypotheses for determining of there is a difference in the proportion of adults who purchase popcorn in each age group. (b) Calculate the test statistic. (c) Calculate the p-value. (d) Interpret the p-value. (e) State your conclusion. (f) Would a confidence interval for the difference in proportions contain zero? Explain without constructing the interval. 91. Africa and the Middle East are two of the least popular regions traveled to in study abroad programs. Suppose a random sample of 250 college students found that 10 traveled to Africa for study abroad. A second random sample of 375 college students found that 10 studied in the Middle East. Is there evidence that more students study abroad in Africa than the Middle East? Perform the appropriate test and include all steps.

Question

Question 91 

7.11 Topic 11:
Inference for Two Proportions
88. The Vegetarian Resource Group commissioned Harris Poll in 2016 to conduct a nationally rep-
resentative online poll of 2,015 American adults aged 18 and over. They found that 3.3% of the
respondents identified as vegetarian.
Food habits in India tend to have a large religious and social component. How does the popularity
of the vegetarian diet differ in the US and India? A 2014 survey conducted by the Registrar
General of India found that 29% of Indians were vegetarian. Suppose the proportion was obtained
from a random sample of 1,000 Indians.
(a) Construct and interpret a 99% confidence interval for the difference in proportions of
tarians in India and the US.
vege-
(b) Based on the interval, what kind of evidence do you expect to have for the alternative in a
two-sided hypothesis test? Explain.
89. It is hard to persuade consumers to abandon a product with which they are familiar. One
experiment gave consumers free samples of a new laundry detergent and also a standard detergent.
After some time, ask the subjects which detergent they prefer. Here are the data.
User
Nonuser
Prefer new product
Prefer standard product
19
31
29
27
(a) Calculate a 90% confidence interval for the difference in proportions between nonusers and
users of the standard detergent that prefer the new detergent.
(b) Based on the confidence interval in (a), can we conclude that a significant difference exists
between the proportion of nonusers of the standard detergent who prefer the new detergent
and the proportion of users of the standard detergent who prefer the new detergent? Explain.
90. Spending on concessions at the movies varies by age of the movie goer. A random sample of 100
adults in their 40's found that 70 purchased popcorn. A random sample of 100 adults less than
40 years old found that 59 purchased popcorn.
(a) State the hypotheses for determining of there is a difference in the proportion of adults who
purchase popcorn in each age group.
(b) Calculate the test statistic.
(c) Calculate the p-value.
(d) Interpret the p-value.
(e) State your conclusion.
(f) Would a confidence interval for the difference in proportions contain zero? Explain without
constructing the interval.
91. Africa and the Middle East are two of the least popular regions traveled to in study abroad
programs. Suppose a random sample of 250 college students found that 10 traveled to Africa
for study abroad. A second random sample of 375 college students found that 10 studied in the
Middle East. Is there evidence that more students study abroad in Africa than the Middle East?
Perform the appropriate test and include all steps.
Expand
Transcribed Image Text

7.11 Topic 11: Inference for Two Proportions 88. The Vegetarian Resource Group commissioned Harris Poll in 2016 to conduct a nationally rep- resentative online poll of 2,015 American adults aged 18 and over. They found that 3.3% of the respondents identified as vegetarian. Food habits in India tend to have a large religious and social component. How does the popularity of the vegetarian diet differ in the US and India? A 2014 survey conducted by the Registrar General of India found that 29% of Indians were vegetarian. Suppose the proportion was obtained from a random sample of 1,000 Indians. (a) Construct and interpret a 99% confidence interval for the difference in proportions of tarians in India and the US. vege- (b) Based on the interval, what kind of evidence do you expect to have for the alternative in a two-sided hypothesis test? Explain. 89. It is hard to persuade consumers to abandon a product with which they are familiar. One experiment gave consumers free samples of a new laundry detergent and also a standard detergent. After some time, ask the subjects which detergent they prefer. Here are the data. User Nonuser Prefer new product Prefer standard product 19 31 29 27 (a) Calculate a 90% confidence interval for the difference in proportions between nonusers and users of the standard detergent that prefer the new detergent. (b) Based on the confidence interval in (a), can we conclude that a significant difference exists between the proportion of nonusers of the standard detergent who prefer the new detergent and the proportion of users of the standard detergent who prefer the new detergent? Explain. 90. Spending on concessions at the movies varies by age of the movie goer. A random sample of 100 adults in their 40's found that 70 purchased popcorn. A random sample of 100 adults less than 40 years old found that 59 purchased popcorn. (a) State the hypotheses for determining of there is a difference in the proportion of adults who purchase popcorn in each age group. (b) Calculate the test statistic. (c) Calculate the p-value. (d) Interpret the p-value. (e) State your conclusion. (f) Would a confidence interval for the difference in proportions contain zero? Explain without constructing the interval. 91. Africa and the Middle East are two of the least popular regions traveled to in study abroad programs. Suppose a random sample of 250 college students found that 10 traveled to Africa for study abroad. A second random sample of 375 college students found that 10 studied in the Middle East. Is there evidence that more students study abroad in Africa than the Middle East? Perform the appropriate test and include all steps.

Expert Answer

Want to see the step-by-step answer?

Check out a sample Q&A here.

Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.
Tagged in
Math
Statistics

Related Statistics Q&A

Find answers to questions asked by students like you.

Q: A manufacturer of aspirin claims that the proportion of headache sufferers who get relief with just ...

A: Click to see the answer

Q: The stiffness of a certain type of steel beam used in building construction has mean 30 kN/mm and st...

A: Click to see the answer

Q: King Tut was an ancient Egyptian ruler whose tomb was discovered and opened in 1923. Legend has it t...

A: From the given information, Lets significance (α) = 0.05. Hypothesis test:

Q: The owners of the Westfield Mall wished to study consumer shopping habits. From earlier studies, the...

A: 1. Denote μ as the true mean time (hours) spent at the mall. The null and alternative hypotheses are...

Q: It is desired to check the calibration of a scale by weighing a standard 10 g weight 100 times. Let ...

A: Here, the null hypothesis is rejected. Thus, there is enough evidence to conclude that the scale is ...

Q: Question 14

A: From the provided information, Sample size (n) = 36 Population Mean (µ) = 100 Population standard de...

Q: Standard Error of Estimate A random sample of 118 different female statistics students is obtained a...

A: The data show the statistics of 118 different female students paired weights (weight in kg, weight i...

Q: An IQ test is designed so that the mean is 100 and the standard deviation is 16 for the population o...

A: Click to see the answer

Q: Please provide step by step instructions.  If you use a formula please use actual figures. Three ran...

A: Median: The median is the middle value in an ordered sequence of data. If there are no ties, half of...

Q: A chocolate chip cookie manufacturing company recorded the number of chocolate chips in a sample of ...

A: Click to see the answer

Q: A random sample of n = 9 is obtained from a normal distribution with μ= 40 and σ=15. What is the pro...

A: Click to see the answer

Q: Find the area under the normal curve a) To the left of z = 0.56. b) Between z = −2.93 and z = −2.06....

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for yo...

Q: Suppose P(X1) = .75 and P(Y2|X1) = .40. What is the joint probability of X1 and Y2?

A: Find the joint probability of X1 and Y2. The joint probability is obtained as given below:

Q: The scores of students on the SAT college entrance examinations at a certain high school had a norma...

A: Click to see the answer

Q: The pH of an acid solution used to etch aluminum varies somewhat from batch to batch. In a sample of...

A: a) The null and alternative hypotheses are provided as;

Q: The article “HIV-positive Smokers Considering Quitting: Differences by Race/Ethnicity” (E. Lloyd-Ric...

A: Note: here, MINITAB software is used to obtain the hypothesis test for proportion. In a group of 230...

Q: A man claims to have extrasensory perception (ESP). As a test, a fair coin is flipped 2323 times, an...

A: Note: It is considered that the coin is flipped 23 times and the person gets 20 out of 23 correct.

Q: how to solve this Suppose that you take 1000 simple random samples from a population and​ that, for ...

A: Click to see the answer

Q: Use the given information to find the number of degrees of freedom, the critical values x? and x, an...

A: Click to see the answer

Q: The article "Prediction of Performance and Evaluation of Flexible Pavement Rehabilitation Strategies...

A: Click to see the answer

Q: what is the probability to win buying one ticket at the lottery with 6 out of 56 balls and how many ...

A: Click to see the answer

Q: A population consists of the following five values: 2, 2, 4, 4, 8. List all the samples of size 2, ...

A: According to the provided information, population values are 2, 2, 4, 4, and 8. a) Total observation...

Q: Assume that a sample is used to estimate a population proportion p. Find the 99.5% confidence interv...

A: Click to see the answer

Q: The chair of the board of directors says, “There is a 50% chance this company will earn a profit, a ...

A: Click to see the answer

Q: The April rainfall in Flagstaff, Arizona, follows a uniform distribution between 0.5 and 3.00 inches...

A: Click to see the answer

Q: As part of a quality-control study aimed at improving a production line, the weights (in ounces) of ...

A: Click to see the answer

Q: Suppose that you flip a balanced coin 12 times. What is the probability that you achieve at least 5 ...

A: Click to see the answer

Q: C. d. n= 10, p = 0.40, X = 4 e. n= 12, p = 0.90, X = 2 || %3D || 1. Compute the of X successes, usin...

A: Consider X be a random variable which follows binomial distribution with number of trials, n and the...

Q: A thermocouple placed in a certain medium produces readings within 0.1°C of the true temperature 70%...

A: Total number of independent readings is 10. There is about 70% of the time the readings within of th...

Q: Question 78 Parts A, B, and C

A: (a) In most practical cases, the population parameter of interest is unknown; so, the researchers co...

Q: Sales of a new line of athletic footwear are crucial to the success of a company. The company wishes...

A: Click to see the answer

Q: A ng.cengage.com PowerPoint Chapter 8: CJC/Soc Stats S2020 In-... Mind Tap - Cengage Learning A rand...

A: GivenThe distribution of ratings are normally distributed with standard deviation = 0.84Level of sig...

Q: A large tank of fish from a hatchery is being delivered to a lake. The hatchery claims that the mean...

A: Consider X be a random variable which follows normal distribution indicates the length of fish in th...

Q: Clinical Trials of OxyContin OxyContin (oxycodone) is a drug used to treat pain, but it is well know...

A: From the provided information, Sample size (n1) = 52 + 175 = 227 Let x1 be a random variable which r...

Q: A normal population has a mean of 20.0 and a standard deviation of 4.0. Compute the z value associat...

A: Click to see the answer

Q: The cost of 5 gallons of ice cream has a standard deviation of 7 dollars with a mean of 39 dollars d...

A: Click to see the answer

Q: Can you please solve d,e,f and g and show the steps

A: Click to see the answer

Q: Below indicate whether the appropriate test would be an independent t-test, dependent t-test, One-wa...

A: Click to see the answer

Q: how to compute a z score with table

A: Click to see the answer

Q: A recipe submitted to a magazine by one of its subscribers’ states that the mean baking time for a c...

A: Click to see the answer

Q: In an experiment to test the effectiveness of a new sleeping aid, a sample of 12 patients took the n...

A: The claim is that the mean time to sleep is less for the new drug. The hypotheses can be constructed...

Q: In a certain process, the probability of producing a defective component is 0.07. a) In a sample of ...

A: (a)   The probability that fewer than 20 of the components are defective is 0.7323 and it is calcula...

Q: This exercise shows that the signed-rank test can be used with paired data. Two gauges that measure ...

A: Click to see the answer

Q: Predicting Nicotine in Cigarettes Refer to Data Set 13 “Cigarette Contents” in Appendix B and use th...

A: Note: Thanks for posting the question. We are using the Minitab software to predicting the nicotine ...

Q: A random sample of 50 employees of a large company was asked the question, "Do you participate in th...

A: Click to see the answer

Q: The mean cost of a five pound bag of shrimp is 4646 dollars with a standard deviation of 77 dollars....

A: Given data Mean cost of bag (µ) = 46 Standard deviation = 7 Sample size (n) = 49 probability that th...

Q: A normal population has a mean of 60 and a standard deviation of 12. You select a random sample of 9...

A: Click to see the answer

Q: An engineer takes a large number of independent measurements of the length of a component and obtain...

A: Click to see the answer

Q: The following MINITAB output presents the results of a hypothesis test for the difference Hx - Hy be...

A: The values missed in the table will be obtained as given below: (a)